The Passenger Model (HEINITZ, 2000)

3 The Passenger Model (HEINITZ, 2000)

3.1Underlying Ideas

Without taking this influence into consideration, an insufficiently specified modal split model may wrongly predict the expected increase in the railway market share, thus overestimating the railways revenue aspirations. Treating the problem in the classical context of discrete choice models, for example, means

- to segment the model into a number of new estimation models and / or

- to introduce a new explanatory variable and / or

- to generalize the functional form, e.g. through Box-Cox, Box-Tukey or IP transforms.

At the beginning, there was not any doubt that the traditional procedure could satisfactorily model the status quo. But later it failed to reproduce the results in a case study. The model was not in position of giving a credible answer, why the mobility pattern of typical German households (suburban locations, with car ownership of at least one) remained nearly unchanged after providing access to high-speed rail. More precisely, there were still too few degrees of freedom to obtain the observed “threshold effect”.

This defined the working hypothesis for a first test of a CLP-based approach: Embedding econometric formulas into a framework linked by explicit constraints rules might enlarge the model scope and improve the predictions. In particular, the work focused on the interdependency of choices regarding the everyday mobility pattern and choices on inter-city travel and the constrained “state transitions” once high-speed train supply is added to the set of options.

As illustrated in Figure 2, the expected choice behavior could then not just be described by a smooth (generalized) Logit curve [A], but rather as an outcome of a process of constraint satisfaction. This means that certain inconsistent valuations / areas are excluded from the axis. Furthermore, any user reaction will be ruled out, instantly switching zero elasticities with respect to changes in the explanatory variable. In certain sections that are in line with the assumed constraints, the choice probability function of a rational decision maker follows the known (generalized) Logit curve [B].

The above-stated consistency requirements, of course, could be validated on a micro-level, i.e. on the basis of activity schedules of persons and households. Underlying survey data, however, is often not available, insecure and behavior is object to changes. However, domains of “valid” or “plausible” solutions can be defined through expert statements and assumptions. Some limits restricting travel demand also result from biological limits of human beings.

Following this logic of demand and supply interaction and of supply and demand consistency, the behavior-based CLP model could be organized in form of an interaction process between the demand and supply side of transportation services.

3.2The Modeling Approach

The modeling approach is very much oriented to such activity-based approaches with different time horizons and individual plans. AXHAUSEN (1998): “Each of these (plans and associated time horizons, F.H.) will influence and constrain the behavior of a traveler, who will switch between these different sets of constraints and maybe sets of preferences over the course of the day, week and months, as each project is tied to different levels of the personality of the person.“

A key characteristic of activity-based models is the study of constraints in the decision process. HAEGERSTRAND (1970) itemizes three types of constraints which “limit the activity options available to individuals“ inside their daily time-space prisms:

• 
  Capability constraints, which are imposed by nature or technology limits, human limitations (sense organs and cognitive system),
  
• 
  Coupling constraints, requiring the presence of another person or some other resource in order to participate in the activity opportunity, or things following pre-determined timetables,
  
• 
  Authority constraints, which are institutionally imposed restrictions, such as office or store hours, and regulations, such as noise restrictions.
  

As the activity patterns of different members of a household are often coupled (consider, for instance, holiday trips of a family) the basic decision-making elements of the CLP model are in fact households. Individual household types are aggregated to some homogenous groups of households. In spite of the mesoscopic model representation, it is possible to state the well-known Haegerstrand Prism (HAEGERSTRAND, 1970) of travel time budget or the corresponding monetary budget in form of constraints imposed on the households. The number of activities by type and the also the total time spent on activities is coded with constraint variables. These schedules, too, are represented in a mesoscopic way; i.e. in form of travel time budgets and number of yearly activities. The mobility program qualifies several types of activities (frequencies, party size) and trip purposes such as job commuting, business trips, leisure and tourism travels.

The supply side is first of all based on an optimal path search procedure in physical networks. This opens the possibility of searching hyper-paths in inter-modal and scheduled-service networks. For each trip, its characteristics in different dimensions could be extracted by summing up, for instance, the travel times along the inter-modal chain.

Through stating the respective constraints it is possible to link the service parameters of the transport system(s) to the decision variables – describing the mobility behavior of the modeled persons and families. Based on the trip-making decisions of the household types, individual trips are aggregated from a mesoscopic to a macroscopic level, thus forming O-D trip matrices. These matrices are then assigned to the links of the transport suppliers. In addition to this main cycle, a matrix estimation through constraint reasoning is facilitated by imposing further sets of constraints in a way that traffic loads of network links, matrix elements as well column / row sums must agree to some extent with traffic counts or observed values (if available). Figure 5 gives a glimpse of the overall model.

The formulation as a constraint network assures consistency between demand side variables and supply sides variables with respect to logical constraints on individual behavior and physical abilities of the infrastructure networks. Note however, that in some cases a definite -unique - solution yet is not found by the loose coupling between constraint variables. A heuristic process – pursuing implicit utility maximization – tries to find suitable activity patterns fitting to the constraint network, which results from the interdependency between variables on constraints. With each model run for a specific time, one aims to bring supply and demand side systems into a consistent (equilibrium) state - although they are both reacting with a built-in delay function, perhaps under incomplete information and by incrementally updating their choices - thus in a constrained environment and subject to personal restrictions, limitations and taste variations.